Simple Harmonic Motion — the Pendulum

For small swings the restoring force is proportional to displacement, so the motion is simple harmonic and the period depends only on the length L and gravity g — not on the bob's mass or (for small angles) the amplitude. Energy trades back and forth: all potential at the extremes, all kinetic at the bottom, the total staying constant unless damping removes it. At large release angles the real period grows slightly beyond the small-angle formula — watch the trace lag.

• Try this: Change the release angle — for small angles the period barely changes (the SHM result).
• Try this: Quadruple the length. The period should double, because T ∝ √L.
• Try this: Lower gravity (a Moon-like g) and watch the swing slow right down.
• Try this: Add damping and watch the amplitude decay while the period stays the same.